Question: Ashley is 6 years older than Gabriela. For the last four years, Ashley and Gabriela have been going to the same school. Six years ago, Ashley was 4 times older than Gabriela. How old is Ashley now?
Explanation: We can use the given information to write down two equations that describe the ages of Ashley and Gabriela. Let Ashley's current age be $a$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $a = g + 6$ Six years ago, Ashley was $a - 6$ years old, and Gabriela was $g - 6$ years old. The information in the second sentence can be expressed in the following equation: $a - 6 = 4(g - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = a - 6$ . Substituting this into our second equation, we get the equation: $a - 6 = 4($ $(a - 6)$ $ -$ $ 6)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $a - 6 = 4a - 48$ Solving for $a$ , we get: $3 a = 42$ $a = 14$.